If the money supply increases and the price level is unchanged interest rates will fall

Economics 401 – Answers to Problems from Chapter 7

Review Questions
1.    Money is the economist’s term for assets that can be used in making payments, such as cash and checking accounts. In everyday speech, people often use the term “money” to refer to their income or wealth, but in economics money means only those assets that are widely used and accepted as payment.
2.    The three functions of money are (1) the medium of exchange function, which contributes to a better-functioning economy by allowing people to make trades at a lower cost in time and effort than in a barter economy; (2) the unit of account function, which provides a single, uniform measure of value; and (3) the store of value function, by which money is a way of holding wealth that has high liquidity and little risk.
3.    The size of the nation’s money supply is determined by its central bank; in the United States, the central bank is the Federal Reserve System. If all money is in the form of currency, the money supply can be expanded if the central bank uses newly minted currency to buy financial assets from the public or directly from the government itself. To reduce the money supply, the central bank can sell financial assets to the public or the government, taking currency out of circulation.
4.    The four characteristics of assets that are most important to wealth holders are (1) expected return, (2) risk, (3) liquidity; and (4) time to maturity. Money has a low expected return compared to other assets, low risk since it always maintains its nominal value, is the most liquid of all assets, and has the lowest (zero) time to maturity.
5.    The expectations theory of the term structure of interest rates is the idea that investors compare bonds with different times to maturity and choose the ones that yield the highest return. In equilibrium, the theory implies that the expected rate of return on an N-year bond should equal the average of the expected rates of return on one-year bonds during the current year and the N–1 succeeding years.
       The expectations theory is not sufficient because on average, long-term interest rates exceed short-term interest rates, in violation of the theory’s implications. To form a more accurate theory, a risk premium must be added to the analysis.
6.    The macroeconomic variables that have the greatest impact on money demand are the price level, real income, and the nominal interest rate on other assets. The higher the price level, the higher the demand for money, since more units of money are needed to carry out transactions. The higher the level of real income, the higher the need for liquidity, and so the higher is money demand. When the nominal interest rate on other assets is high, money demand is low, because the opportunity cost of holding money (that is, the interest you forgo on other assets because you are holding money instead) is high.
7.    Velocity is a measure of how often money “turns over” in a period. It is equal to nominal GDP divided by the nominal money supply. The quantity theory of money assumes that velocity is constant, which implies that real money demand is proportional to real income and is unaffected by the real interest rate.
8.    Equilibrium in the asset market is described by the condition that real money supply equals real money demand because when supply equals demand for money, demand must also equal supply for nonmonetary assets. The aggregation assumption that is needed for this is that we can lump all wealth into two categories: (1) money and (2) nonmonetary assets.
9.    In equilibrium, the price level is proportional to the nominal money supply; in particular it equals the nominal money supply divided by real money demand. Similarly, the inflation rate is equal to the growth rate of the nominal money supply minus the growth rate of real money demand.
10.   Factors that could increase the public’s expected rate of inflation include a rise in money growth or a decline in income growth. With no effect on the real interest rate, the increase in the expected inflation rate would increase the nominal interest rate.
Numerical Problems
1.     For a two-year bond, according to the expectations theory, the interest rate would be the average of the two one-year bonds, which is (6% + 4%)/2 = 5%. Adding the risk premium of 0.5% gives an interest rate on the two-year bond of 5.5%.
       For the three-year bond, according to the expectations theory, the interest rate would be the average of the three one-year bonds, which is (6% + 4% + 3%)/3 = 4.33%. Adding the risk premium of 1.0% gives an interest rate on the three-year bond of 5.33%.
       The yield curve would show the interest rate on a one-year bond of 6%, the interest rate on a two-year bond of 5.55%, and the interest rate on a three-year bond of 5.33%, so it would be downward sloping, which is called “inverted” in the market.

2.     (a)  Real money demand is
              Md/P = 500 + 0.2Y – 1000i
= 500 + (0.2 ´ 1000) – (1000 ´ 0.10)
= 600.
              Nominal money demand is
              Md = (Md/P) ´ P = 600 ´ 100 = 60,000.
              Velocity is
              V = PY/Md = 100 ´ 1000/60,000 = 1 2/3.
        (b)  Real money demand is unchanged, because neither Y nor i has changed.
              Nominal money demand is
              Md = (Md/P) ´ P = 600 ´ 200 = 120,000.
              Velocity is unchanged, because neither Y nor Md/P has changed, and we can write the equation for velocity as
              V = PY/Md = Y/(Md/P).
        (c)  It is useful to use the last expression for velocity,
              V = Y/(Md/P) = Y/(500 + 0.2Y – 1000i).
              (1)  Effect of increase in real income:
                    When i = 0.10,
                    V = Y/[500 + 0.2Y – (1000 ´ 0.10)]
             = Y/(400 + 0.2Y)
             = 1/[(400/Y) + 0.2].
When Y increases, 400/Y decreases, so V increases. For example, if Y = 2000, then V = 2.5, which is an increase over V = 1 2/3 that we got when Y = 1000.
              (2)  Effect of increase in the nominal interest rate:
When Y = 1000, V = 1000/[500 + (0.2 ´ 1000) – 1000i]
= 1000/(700 – 1000i)
= 1/(0.7 – i).
When i increases, 0.7 – i decreases, so V increases. For example, if i = 0.20, then V = 2, which is an increase over V = 1 2/3 that we got when i = 0.10.
              (3)  Effect of increase in the price level:
There is no effect on velocity, since we can write velocity as a function just of Y and i. Nominal money demand changes proportionally with the price level, so that real money demand, and hence velocity, is unchanged.
3.     (a)  Md = $100,000 – $50,000 – [$5000 ´ (i – im) ´ 100]. (Multiplying by 100 is necessary since i and im are in decimals, not percent.) Simplifying this expression, we get
Md = $50,000 – $500,000(i – im).
        (b)  Bd = $50,000 + $500,000(i – im).
              Adding these together we get Md + Bd = $100,000, which is Mr. Midas’s initial wealth.
        (c)  This can be solved either by setting money supply equal to money demand, or by setting bond supply equal to bond demand.
Md = Ms

$50,000 – $500,000(i – im) = $20,000
$30,000 = $500,000 i     [Setting im = 0]
i = 0.06 = 6%
Bd = Bs
$50,000 + $500,000i = $80,000
$500,000i = $30,000
i = 0.06 = 6%
4.     (a)  From the equation MV = PY, we get M/P = Y/V. At equilibrium, Md = M, so Md/P = Y/V = 10,000/5 = 2000. Md = P ´ (Md/P) = 2 ´ 2000 = 4000.
        (b)  From the equation MV = PY, P = MV/Y.
When M = 5000, P = (5000 ´ 5)/10,000 = 2.5.
When M = 6000, P = (6000 ´ 5)/10,000 = 3.
5.     (a)  DP/P = –hY DY/Y = –0.5 ´ 6% = –3%. The price level will be 3% lower.
        (b)  DP/P = –hr Dr/r = –(–0.1) ´ 0.1 = 1%. The price level will be 1% higher.
        (c)  With changes in both income and the real interest rate, to get an unchanged price level would require hY DY/Y + hr Dr/r = 0, so [0.5 ´ (Y – 100)/100] – [0.1 ´ 0.1] = 0, so Y = 102.
6.     (a)  pe = DM/M = 10%. i = r + pe = 15%. M/P = L = 0.01 ´ 150/0.15 = 10. P = 300/10 = 30.
        (b)  pe = DM/M = 5%. i = r + pe = 10%. M/P = L = 0.01 ´ 150/0.10 = 15. P = 300/15 = 20. The slowdown in money growth reduces expected inflation, increasing real money demand, thus lowering the price level.
7.     (a)  With a constant real interest rate and zero expected inflation, inflation is given by the equation
p = DM/M – hY DY/Y. To get inflation equal to zero, the central bank should set money growth so that DM/M = hY DY/Y = 2/3 ´ .045 = .03 = 3%. Note that the interest elasticity isn’t relevant, since interest rates don’t change.
        (b)  Since V = PY/M, DV/V = DP/P +DY/Y – DM/M
= 0 + .045 – .03
= .015
              So velocity should rise 1.5% over the next year.
Analytical Problems
1.     (a)  People would probably take money out of checking accounts and put it into money market mutual funds and money market deposit accounts. Money market mutual funds and money market deposit accounts are included in M2 but are not part of M1. The result is a decrease in M1, but no change in M2. M2 does not increase because M1 is part of M2, so the decrease in M1 offsets the increase in the rest of M2.
        (b)  This would reduce both M1 and M2, as people would have reduced need for money in checking accounts, and home equity lines of credit are not included in either M1 or M2.
        (c)  If people fear a stock market collapse, they will want greater liquidity, so they will hold more money. Also, since stocks are an alternative asset to money, and the expected return to stocks has fallen, money demand will increase. Both effects will lead to people investing less in stocks and more in cash, checking accounts, and other items that provide liquidity and safety, so M1 and M2 will both rise.
        (d)  People would have less need for money in checking accounts, and would put more in savings deposits. So M1 will decrease, while M2 will remain unchanged. (Again, M1 is part of M2, so reducing the amount that is in M1, and increasing the amount that is in M2 but not in M1, has no effect on M2.)
        (e)  If currency demand falls, this decreases M1, thus also decreasing M2.
2.   The general rise in velocity from 1959 to 1980 is most likely due to changes in income, in interest rates, and in financial institutions. Higher income led to a less than proportional rise in real money demand, so velocity increased. Rising inflation and rising nominal interest rates in this period led people to seek alternatives to non–interest-bearing money, such as money market mutual funds. The result was lower money demand, and thus higher velocity. Financial innovations also reduced the need for money. Examples include the development of cash management accounts and the use of automated teller machines.
3.     (a)  New cigarettes mean an increase in the money supply. With higher nominal money supply and no change in real money demand, the equilibrium price level must rise.
        (b)  If people anticipate prices rising when the new cigarettes arrive, they will hold less money so that they will not lose purchasing power when prices go up. But if their real money demand is reduced, with the same nominal money supply the equilibrium price level must rise. The result is that when prices are anticipated to rise in the future, people may take actions that cause prices to rise immediately.
4.     (a)  A temporary increase in government purchases reduces national saving, causing the real interest rate to rise for a fixed level of income. If the real interest rate is higher, then real money demand will be lower. So prices must rise to make money supply equal money demand. The result is that output is unchanged, the real interest rate increases, and the price level increases.
        (b)  When expected inflation falls, real money demand increases. With no effect on employment or saving and investment, output and the real interest rate remain unchanged. With higher real money demand and an unchanged nominal money supply, the equilibrium price level must decline. So output and the real interest rate are unchanged and prices decline.
        (c)  When labor supply rises, full-employment output increases. Also, with higher output, saving will increase, so the real interest rate will decline. Both higher output and a lower real interest rate increase real money demand. The price level must decline to equate money supply with money demand. The result is an increase in output and a decrease in both the real interest rate and the price level.
        (d)  When the interest rate paid on money increases, real money demand rises. With no effect on employment or saving and investment, output and the real interest rate remain unchanged. With higher real money demand and an unchanged nominal money supply, the equilibrium price level must decline. So output and the real interest rate are unchanged and prices decline.

What happens when the money supply increases?

What happens to money supply when interest rates fall?

Why does interest rate fall when money supply increases?

What happens to the interest rate if the money supply increases or decreases and the money demand remains unchanged?